The broad, long-term objectives of this project are to develop efficient computational methods for linkage analysis and to investigate the theoretical advantages of having a high density of markers in the mapping of trait genes. It is well known that using multiple markers in a linkage analysis increases the power to establish the chromosome on which the trait gene lies. Recent theoretical work demonstrates how a higher density of markers increases the rate of convergence to the true gene location. Moreover, preliminary research suggests that having dense markers reduces some problems caused by model misspecification. Specifically, suppose a quantitative trait is related to two genes lying on the same chromosome, but a monogenic model is fitted. With sparse markers, the analysis may converge to a location in between the two genes. In contrast, with dense markers, the analysis will converge to the location of the gene with a larger effect and also suggest the presence of the other gene. This project aims to acquire a full understanding of this phenomenon which can have important implications for the study of complex disorders. While having multiple markers has many advantages, it leads to serious computational problems for large human pedigrees. A novel method called sequential imputation had been successfully implemented for the analysis of a diabetes pedigree. This project will implement the method in a more flexible manner, further increasing its efficiency and making it applicable for more problems. The method will be tried on both new and historical data sets to study the practical impact of using many markers simultaneously in a single analysis. Computational problems can arise even with a single marker if the pedigree is highly inbred. Recently, the method of blocking Gibbs, which combines the traditional method of exact computations (peeling) with the Monte Carlo method of Gibbs sampling, had been successfully implemented to analyze a highly inbred pedigree of pigs. This project plans to implement blocking Gibbs for inbred human data. Due to qualitative differences between human and pig data, many challenging problems will have to be solved.